Hitherto, polyester multi-filaments have been used for various applications including clothing and industrial raw materials with making the most of their excellent characteristics. As applications for clothing, many companies have studied aiming at obtaining silky feeling as one target. Actually, in a certain field, characteristic feelings which are better than that of silk have been obtained. For example, associated bundles composed of several multi-filaments which have different heat shrinkage characteristics show excellent properties and feelings such as bulge, bulkiness, warm feeling and the like, and have been widely used. However, if all of the multi-filaments which constitute bundles shrink upon heating, it is impossible to maintain sufficient difference in the degree of shrinkage of filaments because of restraint of the construction of knitted or woven fabric, and further knitted or woven fabric is apt to be hardened because of shrinkage of the filaments. In order to solve such problems, "metsuke (weight)" can be reduced to provide shrinkage characteristic, or alkali reduction can be increased to maintain feeling. However, filaments having great heat shrinkage may generally become stiff by heat treatment and, therefore, products having sufficient feeling can hardly be obtained.
On the other hand, composite bundles composed of polyester filaments which extend by heat treatment and filaments which shrink by heat treatment have been known (e.g., Japanese Patent Laid Open Publication Nos. 62240/1980, 112537/1981, 28515/1985 and the like). These provide much softer and more flexible feeling than the above filaments composed of shrinkable filaments alone. However, they have drawbacks. For example, they become slimy because of loops of elongated and protruded filaments, or handling properties in post treatment are deteriorated because of great difference in length of filaments due to heat treatment, which results in split of filaments.